DProject: Scenario three (The "White and Black" bag):
-If I picked a white marble, I know I'm holding the "White" bag. Since the labels are incorrect in each of the bags, then the "Black" bag must be the real "White and Black" bag. And the "White" bag must be the real "Black" bag.
-If I picked a black marble, my bag must be the "Black" bag. Again, each of the labels are incorrect; that means the bag that says "Black" is actually "White". The bag that says "White" is actually "White and Black".
So, if you're given a task such as this, you should pick a marble from the bag that says it sports both colors. Hope I didn't screw up anything in the final explanation :D
Second post in this thread, sorry about that.
And I'm sorry, but you are over-thinking the problem, remember this is an early elementary school problem (though I probably also worded it poorly). The conclusion is the correct one, you should pick the one from the bag that says that it contains black & white, though as all labels are incorrect, that means that the bag that says black don't contain black marbles, same is true for the white one (but for white), so by picking a marble from the black & white bag you can tell what it contains (i.e. black or white marbles, as it won't contain both)